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      Structural Characterization of Many-Particle Systems on Approach to Hyperuniform States

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          Abstract

          We explore quantitative descriptors that herald when a many-particle system in d-dimensional Euclidean space Rd approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes n terms of the ratio B/Aa, where A is "volume" coefficient and ABis"surfacearea"coefficientassociatedwiththelocalnumbervariance\sigma^2(R)forasphericalwindowofradiusR.TocomplementtheknowndirectspacerepresentationofthecoefficientBintermsofthetotalcorrelationfunctionh({\bf r}),wederiveitscorrespondingFourierrepresentationintermsofthestructurefactorS({\bf k}),whichisespeciallyusefulwhenscatteringinformationisavailableexperimentallyortheoretically.Weshowthatthefreevolumetheoryofthepressureofequilibriumpackingsofidenticalhardspheresthatapproachastrictlyjammedstateeitheralongthestablecrystalormetastabledisorderedbranchdictatesthatsuchendstatesbeexactlyhyperuniform.UsingtheratioB/A,thehyperuniformityindexHandthedirectcorrelationfunctionlengthscale\xi_c,westudythreedifferentexactlysolvablemodelsasafunctionoftherelevantcontrolparameter,eitherdensityortemperature,withendstatesthatareperfectlyhyperuniform.Weanalyzeequilibriumhardrodsand"sticky"hardspheresystemsinarbitraryspacedimensiond$ as a function of density. We also examine low-temperature excited states of many-particle systems interacting with "stealthy" long-ranged pair interactions as the temperature tends to zero. The capacity to identify hyperuniform scaling regimes should be particularly useful in analyzing experimentally- or computationally-generated samples that are necessarily of finite size.

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          Author and article information

          Journal
          27 March 2021
          Article
          2103.14989
          6e90eaa9-0416-45a6-b0c9-7b7e178b7fc5

          http://creativecommons.org/licenses/by/4.0/

          History
          Custom metadata
          19 pages, 14 figures
          cond-mat.soft cond-mat.mtrl-sci cond-mat.stat-mech

          Condensed matter
          Condensed matter

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